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Sagot :
The mass of one metal atom is [tex]1.770\times 10^{-22}[/tex]grams.
The metal atom is palladium.
Explanation:
Given:
A face-centered unit cell.
The density of the unit cell is [tex]12020 kg/m^3[/tex].
The edge length of the unit cell 389.08 pm
To find:
The mass of one atom of the metal
Solution:
The density of the unit cell = d = [tex]12020 kg/m^3[/tex]
The edge length of the unit cell = a = 389.08 pm
[tex]1 pm = 10^{-12} m\\a=389.08 pm=389.08\times 10^{-12} m=3.8908\times 10^{-10}m[/tex]
Total number of atoms in F.C.C unit cell = z = 4
The atomic mass of the metal atom = M
The density of the unit cell is given by:
[tex]d=\frac{z\times M}{N_A\times a^3}\\12020 kg/m^3=\frac{4\times M}{6.022\times 10^{23}mol^{-1}\times (3.8908\times 10^{-10}m)^3}\\M=0.106586 kg/mol\\1 kg=1000 g\\M=0.106586 kg/mol=0.106586 \times 1000 g/mol\\M=106.586 g/mol[/tex]
The mass of one mole of metal atom = 106.586 g
The mass of 1 atom of metal :
[tex]=\frac{106.586 g}{6.022\times 10^{23}}\\=1.770\times 10^{-22} g[/tex]
The mass of one metal atom is [tex]1.770\times 10^{-22}[/tex] grams.
The atomic mass of the metal atom is 106.586 g/mol which is close to the atomic mass of the palladium. Hence, the metal atom is palladium.
Learn more about the density of unit cell here:
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